The R script in this repository does Local Density Analysis, as implemented in the LDEN.exe program in Keith Kintigh's Tools for Quantitative Archaeology (TFQA). The method is described in Johnson (1984:83-85) and Kintigh (1990), as well as in the TFQA documentation. The original description of the method is apparently in Johnson's (1976) thesis from the University of Bordeaux, but I have not been able to obtain a copy. (Presumably there is a copy at the University of Bordeaux, but all WorldCat shows are two listings at DAI (one for "DAI, Eurasien Abteilung"; one for "DAI RGK, Frankfurt am Main"))

The R script currently includes five functions that produce a dataframe containing local density coefficients (generated by lda(), which depends on the other functions). The other functions return various forms of intermediate data: distance_matrix() returns a square matrix of the distances from every point in the data file to every other point;

local_counts() returns a dataframe with the counts, by type, of points within the specified distance of each point (the distance is specified by the argument 'radius')

local_density() returns a dataframe (formatted the same as the one produced by local_counts) in which the counts are divided by the area of the circle defined by the specified radius

glb_density() returns a vector of the global densities of points of each type. The global density is the number of points of the type divided by the total site area.

lda() directly uses the dataframe from local_density() and the vector of global densities from gld_density() to calculate intratype and between-type local density coefficients, with the local density coefficient from Type A to Type B defined as the mean density of points of Type B within the specified radius of points of Type A, divided by the global density of points of Type B.

==================================================================== Things that need to be done with the code

The R script needs to be converted to a package, and there are some functions that need to be added.

THe most complicated addition is an extension of local density analysis described in Kintigh (1990), in which the neighborhood compositions of the points are used as input for cluster analysis (with each individual point as a case, and variables are the percentages (or alternatively counts?) of the types within the local neighborhoods. The points can then be plotted (using their xy coordinates) distinguished by cluster membership (In Kintigh (1990), he plots numbers to show cluster membership (see his Figure 22 on page 194), but different symbols or colors could also work). local_counts() is a separate function (rather than internal to local_density() ), because it outputs the neighborhood composition data that will be needed as input to for cluster analysis.

Another (easier) functions that needs to be added is one to plot the local density coefficients by radius. This was implemented in TFQA by LDPLT.exe, which plots a series of lines (one for each type) with radius on the x axis and the local density coefficient on the y axis.

==================================================================== Resources for Testing the Code

The repository also includes two data files, and output from the original TFQA program LDEN.exe for the data in the files.

One of the data files, LDEN.csv was included with TFQA as a test file. It has data for 16 points and seven types (types are designated using the numbers 0, 2, 4, 10, 11, 12, and 13). As far as I know, the data is made up.

#'AZ_A1020_BLM_point_plots.csv' contains point location and type data for 358 "diagnostic" surface artifacts from an Ancestral Pueblo site on the Shivwits Plateau in northwestern Arizona. In the Arizona site numbering system, the site number is formally "AZ A:10:20 (BLM)", so part of the overly long file name is a actually simplification of that. This is real data, although somewhat simplified here, and not organized quite as I would organize it for a real analysis. There are five types (three of them rare), and the two most common 'types' group artifacts that have more detailed identifications ("ceramics" = either painted potsherds or sherds from vessel rims; "stone tool" = any flaked stone tool except for projectile points).

For each data file there are four matching files of output from LDEN.exe: the .txt files contain the local density coefficients for radii of 1, 2, and 5 meters. The .out files have the counts for the local neighborhoods of each point. The R script formats the output differently, but if you run the code at the end of the script, lda_test should have the same local density coefficients as the .txt file that used the same data. Similarly, counts_test should have the same counts as the .out file that uses the same data and radius.

LDEN.exe expects the type designations to be numbers, so the AZ_A1020... output from LDEN.exe shows types 1-5 rather than descriptive type names. The numbers correspond to the types in the .csv in alphabetical order (1 = bead, 2 = ceramic, 3 = groundstone, 4 = projectile point, 5 = stone tool). The types should be in the same order in all the output files.

==================================================================== References

Johnson, Ian 1976 Contribution méthodologique a l'étude de la répartition des vestiges dans des niveaux archéologiques. DES (Diplome des Études Superieurs) Thesis, Universite de Bordeaux I.

1984 Cell Frequency Recording and Analysis of Artifact Distributions. In Intrasite Spatial Analysis in Archaeology, edited by Harold Hietala, pp. 75-96. University of Cambridge Press.

Kintigh, Keith W. 1990 Intrasite Spatial Analysis: A Commentary on Major Methods. In Mathematics and Information Science in Archaeology: A Flexible Framework, edited by Albertus Voorrips, pp. 165-200. Holos, Bonn.